In the circuit shown below,
(a) Write a node equation at node 1 by summing the currents leaving node 1.
(b) Write a node equation at node 2 by summing the currents leaving node 2.
(c) Find V1 and V2 by solving the two node equations.
(d) Find the currents IR1, IR2, IR3, IR4, I5.
(e) Find the power absorbed by R1, R2, R3, R4, and power released by Vs and Is.
R1=2000;R2=3000;R3=500;R4=1000;
Vs=8;Is=4e-3;
3
syms V1 V2
[V1,V2]=solve(-Is+(V1-Vs)/R1+(V1-V2)/R2,...
(V2-V1)/R2+V2/R4+(V2-Vs)/R3,V1,V2);
IR1=(V1-Vs)/R1;
IR2=(V1-V2)/R2;
IR3=(Vs-V2)/R3;
IR4=V2/R4;
I5=IR3-IR1;
PR1=IR1^2*R1;
PR2=IR2^2*R2;
PR3=IR3^2*R3;
PR4=IR4^2*R4;
PVs=-I5*Vs;
PIs=-Is*V1;
Pa=PR1+PR2+PR3+PR4;
Ps=PVs+PIs;
Psum=PR1+PR2+PR3+PR4+PVs+PIs;
V1=vpa(V1,7)
V2=vpa(V2,7)
IR1=vpa(IR1,7)
IR2=vpa(IR2,7)
IR3=vpa(IR3,7)
IR4=vpa(IR4,7)
I5=vpa(I5,7)
PR1=vpa(PR1,7)
PR2=vpa(PR2,7)
PR3=vpa(PR3,7)
PR4=vpa(PR4,7)
PVs=vpa(PVs,7)
PIs=vpa(PIs,7)
Pa=vpa(Pa,7)
Ps=vpa(Ps,7)
Psum=vpa(Psum,7)
Answers:
V1 =
12.0
V2 =
6.0
IR1 =
0.002
IR2 =
0.002
IR3 =
0.004
IR4 =
0.006
I5 =
0.002
PR1 =
0.008
PR2 =
0.012
PR3 =
0.008
PR4 =
0.036
PVs =
-0.016
PIs =
-0.048
Pa =
0.064
Ps =
-0.064
Psum =
0.0
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